combining objects in logic editor
What your final result may look like:





You can link the logic-bricks of different objects if you select both of these objects in the 3d-view.



In my example, I use a mouse-over and a left-button sensor to detect a click on the handle. That goes to an and-controller, which is connected to both the armature of the door and the armature of the handle. Both armatures then play their animation.